Controllable Chiral Light Generation and Vortex Field Investigation Using Plasmonic Holes Revealed by Cathodoluminescence

Control of the angular momentum of light is a key technology for next-generation nano-optical devices and optical communications, including quantum communication and encoding. We propose an approach to controllably generate circularly polarized light from a circular hole in a metal film using an electron beam by coherently exciting transition radiation and light scattering from the hole through surface plasmon polaritons. The circularly polarized light generation is confirmed by fully polarimetric four-dimensional cathodoluminescence mapping, where angle-resolved spectra are simultaneously obtained. The obtained intensity and Stokes maps show clear interference fringes as well as almost fully circularly polarized light generation with controllable parities by the electron beam position. By applying this approach to a three-hole system, a vortex field with a phase singularity is visualized in the middle of three holes.


Main
Control of angular momentum of light is one of the crucial technologies to realize nextgeneration nano-optical devices and optical communications, including quantum communication and encoding, [1][2][3][4] and has been extensively investigated in topological photonic structures or for coupling to the electron spins in materials.Spin angular momentum (SAM) of light is represented by left-or right-handed circularly polarized light (CPL), which is a robust signal carrier and has already been practically utilized e.g. in 3D cinemas to send two distinct signals for right and left eyes regardless of the observation angle.For a macroscopic CPL parity control, a linear polarizer and a quarter waveplate are typically combined as a set of filters, which requires much larger scale elements than the light wavelength.For micro or nanoscale devices, it has been proposed to couple a chiral optical nanoantenna with a light source to select the CPL parity by the structure.[5][6][7] This antenna coupling strategy is useful because a linearly polarized light source can be utilized, instead of a CPL-selective source which is not readily available, when coupled with such chiral antennas.However, when the light source is fixed to the structure, dynamic control of CPL is not straightforward because the chirality is fixed to the antenna geometry.To overcome this problem, achiral nanoantennas combined with an optical waveguide have been proposed, where the optical signal from different directions along the waveguide determines the generated CPL parity.[8] This is based on an elaborate fabrication of optical waveguides with coupled nanoantennas and highly efficient propagation of light is required.As an alternative approach, CPL generation using an electron beam, or cathodoluminescence (CL), has been proposed, which is possible even from a spherical particle by controlling the phase difference of two dipoles in the structure.[9][10][11] Such electron beam-based light generation is expected to be a scheme for prospective laser or quantum light sources.[12,13] Although the use of the electron beam for optical devices requires different technologies compared to purely light-based systems and may give limitations, the electron-beam approach is not unrealistic as there have been various table-top devices with electron beams, such as cathode-ray tubes, streak-cameras, short-wavelength light sources, indicating the practical applicability of this approach.While integrated photonics facilitate the production of the light sources and would realize photonic circuits [7,8,14], electron-beam-based technology can offer extremely fast switching, [12] as is already used in fast cameras.
Here we propose a new approach to generate CPL using circular metallic holes coupled to surface plasmon polaritons (SPPs), that is a different mechanism compared to the previous studies.Plasmonic hole structures are useful antennas since SPP is already incorporated in the structure working as a guided wave on the surface.In such structures, transition radiation (TR) and SPP scattering field, which are generated at spatially separate locations, leads to interference; When an electron beam is irradiated onto the metal film, away from the antenna structures, TR is generated at the electron beam position and simultaneously and coherently excited SPPs are scattered by the antenna and creates photons.Since all the interaction processes are coherent with respect to the electron excitation, the light from these two sources interferes.[15] Such interferences with TR have given a way to access the phase of the field in the CL measurement.[16] In this study, we utilize this interference of TR and the light through SPP scattering at the hole to control CPL (Fig. 1a).Also using this CPL generation tool with an electron beam, we further visualize a vortex field generation from three holes, emulating a three-phase optical field motor, which corresponds to the orbital angular momentum (OAM) in the SPP field.Holes are fabricated on a free-standing silver membrane by colloidal lithography with a film transfer method.[17,18] The "upside" of the silver membrane is covered by SiO2 to avoid degradation, and the "downside" is covered by carbon so that SPP propagates only along the upside of the membrane (Fig. 1b).A scanning transmission electron microscopy (STEM) CL system is used to evaluate the CPL generation from circular silver holes.The four-dimensional (4D) Stokes data acquisition in this setup allows simultaneous angle-and wavelength-resolved CL mapping, as illustrated in Fig. 1d and e. [9] Figure 2 shows CL mapping results of a 500 nm silver hole with p-polarization at various detection angles θ and photon wavelengths.These CL maps are obtained by scanning the electron beam two-dimensionally on the sample and the CL signal is plotted in synchronization with the beam scan.The left and right halves of the CL maps with symmetric detection angles are shown, namely pairs of θ = 45°, 135° and pairs of θ = 30°, 150°, facing each other in order to compare their interference fringe patterns.The interference fringe pattern is formed clearly at the top and bottom of the images with different fridge pitches, which are also dependent on the wavelength and detection angles.These fringe patterns can be understood as the interference between TR and the scattering from the hole through SPP propagation, as schematically illustrated in Fig. 2a.[16] The phase difference  of TR and the scattered wave from the hole generates the interference fringe patterns.The phase difference  can be expressed using the electron beam position R from the center of the hole as, where   is the SPP wave vector,  is the free-space light wave vector, and  is the azimuthal angle of the position. corresponds to an additional phase shift related to the excitation of the TR and the scattering of the SPP by the hole.The interference patterns have shorter pitches in the upper half of the image (x > 0) than the lower half (x < 0), which is because the sign of the TR phase shift (second term in Eq.1) flips with respect to SPP-scattering light (first term in Eq.1), as illustrated in Fig. 2a.The comparison of the maps with symmetric detection angles with respect to the sample plane reveals that the fringe pattern does not match for the symmetric pairs (θ = 45°, 135° pair in Fig. 2b and θ = 30°, 150° pair in Fig. 2c).This mismatch is related to the phase difference of the TR towards the top (θ < 90°) and bottom (θ > 90°) spaces, contributing to the offset  in Eq.1.This phase difference between the top-ward and the bottom-ward TRs is approximately π when the space is separated by an ideal metal film producing mirror-symmetric dipole radiations.
To better understand the behavior of TR, we calculated the electromagnetic field distribution by 80 keV electron moving in and out of a silver surface, as shown in Figure 2d.[19] One can see TR emitted into the free space and SPP propagating on the surface, as described in the scheme of Fig. 2a.Since the TR is an effective electric dipole polarized perpendicular to the interface, the transverse magnetic field, as plotted in Fig. 2d, well represents the phase of the TR field.The zero phase is set when the electron is located at the interface.As clearly seen, the phase difference is ~π, which can be slightly shifted due to the presence of the carbon layer.The theoretically calculated TR phase from a carbon surface is also shown in the Supporting Information.While TR can be approximated by a perpendicular electric dipole, the field from a hole in a metallic film can be described by a magnetic dipole [20][21][22][23], which e.g. has the magnetic polarization along the yaxis when the electron beam is placed on the x-axis as in the configuration of Fig. 2a.This scattering field from the hole magnetic dipole gives symmetric magnetic distributions on the top (z-positive) and back (z-negative) sides of the sample, as shown on the right of Fig. 2d.Thus, the radiations by TR and hole scattering differently interfere in the top (z-positive) and back (znegative) side hemispheres of the space, generating shifted interference patterns as in the experiment in Fig. 2b and c.In the upside-down configuration of the sample, as shown in Figure 2e, the interference pattern shifts only slightly.This indicates that the phase shifts of the SPP and TR excitations by flipping the sample cancels out the total phase offset delta together with the influence of the carbon layer.Considering that the interference between TR and SPP-mediated scattering gives nice fridge patterns for p-polarization mapping revealing the phase difference between TR and hole scattering, one can utilize this interference to produce CPL when the s-polarization component in the hole scattering is included.Although CPL cannot be produced in a system with a point symmetry, the symmetry of this circular nanohole system can be broken by the electron beam position, detection angle, and polarization, i.e. by so-called extrinsic chirality.[9,10] We analyze these CPL properties by calculating Stokes parameters from six CL mapping images with different polarizations, namely p-polarization, s-polarization, +45°-polarization, -45°-polarization, RCP, and LCP (see Fig. 1d, e for the parameter definition).The six images with different polarizations are obtained separately by scanning the electron beam over the same area of the sample and the exact position of each image is aligned and normalized for the Stokes parameter calculation.More details of the procedure is described in Supporting Information as well as in the previous study.[9] The representative Stokes mapping results are shown in Fig. 3 for different detection angles and wavelengths.In all the maps, interference fringe patterns due to TR and hole scattering are visible.
Similarly to the interference patterns in Fig. 2, these fringe patterns become asymmetric with respect to the y-axis (horizontal axis) when the detection angle is off the z-axis, as suggested by eq. 1.
In the S3 (RCP-LCP signal) maps in Fig. 3, both LCP (blue) and RCP (red) generations are confirmed, which are all mirror-symmetric with a flipped sign with respect to the x-z plane (vertical line at the center of the image).This symmetry can be understood from the inclusion of the mirrorsymmetric electric field with a flipped sign against the x-z plane of the hole magnetic dipole polarized along the x direction when the electron beam is located off the center of the hole.Since the electric field of TR is symmetric with respect to the x-z plane, the interference between the TR and hole scattering generates CPL together with the interference fringe patterns corresponding to the phase difference between TR and hole scattering.
The δ maps, showing the phase difference between the p-polarization and s-polarization components, and the η maps, corresponding to CPL "circularity", show that almost perfect CPL While the radiation field from a hole in a metal film corresponds to the field distribution of a magnetic dipole, [20][21][22][23] the SPP field on the film generated by the hole can be treated as an inplane-polarized electric dipole in the 2D space.We here utilize this hole dipole on the surface as an SPP field source to generate a vortex field on a surface, corresponding OAM in the SPP field, and visualize this field rotation by Stokes mapping.We demonstrate this vortex generation using three holes aligned as shown in Fig. 4. We chose this configuration with one large hole and two smaller ones to ascertain a strong SPP scattering field in the middle of the three with different phases to create a vortex.When a plane wave is illuminated, such holes within the illumination field will be coherently excited with some phase differences for a given illumination angle.Due to the reciprocity of the wave, CL measurement with a certain detection angle θ corresponds to the z-field measurement generated by such plane wave illumination with an angle θ, as illustrated in Fig. 4a.(see also the Supporting Information) Thus, we can reasonably analyze the wave interference from the three holes by CL field mapping as the generated field from the holes reciprocally.Such a rotating field from three field sources with certain phase differences can be understood from the concept of a three-phase motor, as described in Fig. 4b.
The measured CL maps with θ = 30° and λ = 660 nm are shown in Fig. 4c-g for different polarization conditions and representative Stokes parameters.The Stokes maps are reproduced from six images of different polarizations by scanning the electron beam over the sample, in the same manner as the results of Fig. 3. Clearly, interferences of SPPs from the holes are observed in the positions between the holes, generating a more complicated field distribution compared to the single hole case.Closely looking at the s-pol field map and the δ map (Fig. 4g), one finds a position with a phase singularity in the middle of the three holes, which is marked by dashed circles.At this position, we expect field interferences of these three sources.The phase pattern (Fig. 4g) gives a rotating phase and no amplitude (Fig. 4d) at the center of this rotation is found, which are the typical features of the phase singularity of the vortex fields.
To compare with the experimental results and confirm the vortex field, analytically calculated field distributions are shown in Fig. 4h-m.In this model, three dipole sources on a 2D plane are excited by a plane wave with an incidence angle of θ = 30°, which is reciprocal to the CL measurement (Fig. 4a).To introduce the additional field of the TR in the analytical calculation, a plane wave field over the surface of the calculation plane is overlaid (see calculation details in Supporting Information).The analytical calculation patterns in Fig. 4j-m well reproduce the experimental results, as seen in the pitch and position of the interference fringes in the p-pol and S3 maps (Fig. 4d, e, j, k) as well as the field singularity in the s-pol maps (Fig. 4d, j) at the vortex position indicated by the circle and the vortex phase rotation in the  phase maps (Fig. 4g, m).
Although only the phase difference of s-and p-polarizations (not each phase) is available in the experiment, according to the analytical calculation, the p-pol phase in Fig. 4i is dominated by TR (plane wave on the surface) constantly shifting in the x direction, with almost no local variation originating from the p-polarized dipole field from each hole.Thus, this CPL phase measurement basically extracts the phase of s-polarized (horizontally polarized) dipoles.The local variation of the relative phase δ (Fig. 4g, m) corresponds to the s-polarization phase (Fig. 4h) spread on the homogeneous background with a constant inclination of the p-polarized TR phase.(Fig. 4i).
At the vortex field position, as marked by circles in Fig. 4j, m in the middle of the three holes, the simulated singularity features well correspond to the experimental ones in the experiment (Fig. 4 d,g).Since this field singularity is mainly of the s-polarized (horizontally polarized) dipole fields (Fig. 4h), it is natural that only the s-pol field gives zero amplitude at this singularity point (Fig. 4d,j) while the field in non-zero at this position in the p-pol field patterns (Fig. 4e,k).This singularity at the vortex center is also confirmed by the well-corresponding phase plots of s-pol and δ in Fig. 4h, m.In SI, the rotating phase reproduced by simulation is shown.Thus, we have visualized the SPP vortex field generated from three holes, demonstrating a three-phase field motor.
This demonstrates that such a vortex field can be generated in a much simpler way than highly organized nanostructures.We correct the position shift of the image of each polarization, which is caused by sample drifting, and normalize the intensity of the photon map of each polarization.The position of each photon map is adjusted so that the simultaneously obtained STEM images completely overlap.The intensity normalization of each image is also performed for the Stokes calculation, assuming the following two conditions: 1) The integrated intensity over all the mapping area is equal to that of the geometrically symmetric measurement with respect to the xz-plane, namely ∬  45°  = ∬  −45°  and ∬    = ∬   .
These conditions originate from the symmetry of the measurement system with respect to the xzplane.The above formulations deduce simpler normalization relations of the integrated intensities for ±45° and circular polarizations as ∬  45°  = ∬  −45°  = ∬    = ∬   .

S6. Signal intensity
Figure S5a shows the emission probability of TR and SPP on a silver surface calculated for 80 keV electron according to the literature.[1] With the electron beam current of 1 nA, as used in this study, the generated photons by TR are ~ 2 × 106 /s for the shown wavelength range (400-750nm).The rate of SPPs is calculated as ~ 6 × 106 /s in the same wavelength range.The number of the detected photons are reduced by selecting the wavelength range and the detection solid angle.As SPPs propagate from the electron beam position toward the hole in a circular S7 manner, the SPP intensity is reduced by the distance as well as by the material loss, as shown in Fig. S5b.For the longer wavelength range (>500 nm), the propagation length is large enough, indicating that the material loss is not significant for this measurement.In contrast, the loss effect is more clearly visible for the plots of 400 nm wavelength in Figs.

Figure 1 .
Figure 1.Concept and method of the study.(a) Illustration of circularly polarized light generation

Figure 2 .
Figure 2. CL mapping of a 500 nm single silver hole with p-polarization, i.e. polarized in the x-z

(Figure 3 .
Figure 3. Circularly polarized light generation from a 500 nm single silver hole in various [24]

Figure 4 .
Figure 4. Vortex field generation using three holes.(a) Schematic illustration of monitoring the

Figure S2 .
Figure S2.(a) Illustration of the reciprocity between far-field cathodoluminescence detection (left) 2 and 3 in the main text.

Figure S5 .
Figure S5.(a) Emission probability of TR and SPP on a silver surface calculated for 80 keV